Exact algorithms for dominating set

Rooij, Johan M. M. van; Bodlaender, Hans L.

doi:10.1016/j.dam.2011.07.001

Cited by 73 publications

(26 citation statements)

References 13 publications

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“…Such problems include the Karatsuba algorithm [15] and the Strassen algorithm [23]. Other algorithms which are not analyzed by master theorem but can be sped up using this technique include some exponential recursive algorithms for solving 3-SAT, maximum independent set, as well as other exponential algorithms based on the branch-and-reduce method [21,26].…”

Section: Recursive Algorithmsmentioning

confidence: 99%

Theoretical Model of Computation and Algorithms for FPGA-Based Hardware Accelerators

Hora

Končický

Tětek

2019

Lecture Notes in Computer Science

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While FPGAs have been used extensively as hardware accelerators in industrial computation [20], no theoretical model of computation has been devised for the study of FPGA-based accelerators. In this paper, we present a theoretical model of computation on a system with conventional CPU and an FPGA, based on word-RAM. We show several algorithms in this model which are asymptotically faster than their word-RAM counterparts. Specifically, we show an algorithm for sorting, evaluation of associative operation and general techniques for speeding up some recursive algorithms and some dynamic programs. We also derive lower bounds on the running times needed to solve some problems.

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Section: Recursive Algorithmsmentioning

confidence: 99%

Theoretical Model of Computation and Algorithms for FPGA-Based Hardware Accelerators

Hora

Končický

Tětek

2019

Lecture Notes in Computer Science

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“…The Dominating Set problem ranges among one of the most famous N Pcomplete covering problems [8], and has received a lot of attention during the last decades. In particular, the trivial enumeration algorithm of runtime O * (2 n ) 1 has been improved by a sequence of papers [7,14,23]. The currently best known algorithms for the problem run in time O * (1.4864 n ) using polynomial space, and in time O * (1.4689 n ) needing exponential space [14].…”

Section: Introductionmentioning

confidence: 99%

Exact Algorithms for Weak Roman Domination

Chapelle¹,

Cochefert

Couturier

et al. 2013

Lecture Notes in Computer Science

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International audienceWe consider the Weak Roman Domination problem. Given an undirected graph G = (V,E), the aim is to find a weak roman domination function (wrd-function for short) of minimum cost, i.e. a function f: V → {0,1,2} such that every vertex v ∈ V is defended (i.e. there exists a neighbor u of v, possibly u = v, such that f(u)≥1) and for every vertex v ∈ V with f(v) = 0 there exists a neighbor u of v such that f(u)≥1 and the function f_u → v defined by:f_u→v(x)={1 if x=v,f(u)-1 if x=u,f(x) if x∉{u,v}} does not contain any undefended vertex. The cost of a wrd-function f is defined by cost(f) = ∑ _v ∈ V f(v). The trivial enumeration algorithm runs in time O^∗(3ⁿ) and polynomial space and is the best one known for the problem so far. We are breaking the trivial enumeration barrier by providing two faster algorithms: we first prove that the problem can be solved in O^∗(2ⁿ) time needing exponential space, and then describe an O^∗(2.2279ⁿ) algorithm using polynomial space. Our results rely on structural properties of a wrd-function, as well as on the best polynomial space algorithm for the Red-Blue Dominating Set problem

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“…Exact algorithms to solve the MDS problem can found in Fomin et al (2005); Grandoni (2006);van Rooij & Bodlaender (2011). Particularly, van Rooij & Bodlaender (2011) developed a branch-and-reduce method and obtained good results for the DS problems and variants.…”

Section: Related Workmentioning

confidence: 99%

“…Exact methods and formulations have been proposed mainly for the MCDS problem. These approaches are unable to solve most instances in a reasonable time (van Rooij & Bodlaender, 2011;Lucena et al, 2010;Gendron et al, 2014).…”

Section: Context and Challengesmentioning

confidence: 99%

“…This literature in the cases of solutions with approximation algorithms is discussed in Grandoni (2006), who proposed an algorithm which solves the MDS in O(1.9053 n ) time, where n is the number of vertices in the graph. van Rooij & Bodlaender (2011) proposed an improvement via a complexity for the dominating set regarding the exact algorithm. More specifically, they demonstrated that an algorithm exists that solves the dominating set problem in O(1.4969 n ) time and polynomial space.…”

Section: Related Workmentioning

confidence: 99%

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Matheuristics for Variants of the Dominating Set Problem

ALBUQUERQUE¹

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Exact algorithms for dominating set

Cited by 73 publications

References 13 publications

Theoretical Model of Computation and Algorithms for FPGA-Based Hardware Accelerators

Theoretical Model of Computation and Algorithms for FPGA-Based Hardware Accelerators

Exact Algorithms for Weak Roman Domination

Matheuristics for Variants of the Dominating Set Problem

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